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A320628
Products of primes of nonprime index.
44
1, 2, 4, 7, 8, 13, 14, 16, 19, 23, 26, 28, 29, 32, 37, 38, 43, 46, 47, 49, 52, 53, 56, 58, 61, 64, 71, 73, 74, 76, 79, 86, 89, 91, 92, 94, 97, 98, 101, 103, 104, 106, 107, 112, 113, 116, 122, 128, 131, 133, 137, 139, 142, 146, 148, 149, 151, 152, 158, 161, 163
OFFSET
1,2
COMMENTS
The index of a prime number n is the number m such that n is the m-th prime.
The asymptotic density of this sequence is Product_{p in A006450} (1 - 1/p) = 1/(Sum_{n>=1} 1/A076610(n)) < 1/3. - Amiram Eldar, Feb 02 2021
LINKS
EXAMPLE
The sequence of terms begins:
1 = 1
2 = prime(1)
4 = prime(1)^2
7 = prime(4)
8 = prime(1)^3
13 = prime(6)
14 = prime(1)*prime(4)
16 = prime(1)^4
19 = prime(8)
23 = prime(9)
26 = prime(1)*prime(6)
28 = prime(1)^2*prime(4)
29 = prime(10)
32 = prime(1)^5
37 = prime(12)
38 = prime(1)*prime(8)
43 = prime(14)
46 = prime(1)*prime(9)
47 = prime(15)
49 = prime(4)^2
52 = prime(1)^2*prime(6)
53 = prime(16)
56 = prime(1)^3*prime(4)
58 = prime(1)*prime(10)
61 = prime(18)
64 = prime(1)^6
71 = prime(20)
73 = prime(21)
74 = prime(1)*prime(12)
76 = prime(1)^2*prime(8)
79 = prime(22)
86 = prime(1)*prime(14)
89 = prime(24)
91 = prime(4)*prime(6)
92 = prime(1)^2*prime(9)
94 = prime(1)*prime(15)
97 = prime(25)
98 = prime(1)*prime(4)^2
MATHEMATICA
Select[Range[100], And@@Not/@PrimeQ/@PrimePi/@First/@FactorInteger[#]&]
CROSSREFS
Complement of A331386.
Positions of zeros in A257994.
Primes of prime index are A006450.
Primes of nonprime index are A007821.
Products of primes of prime index are A076610.
Products of primes of nonprime index are this sequence.
The number of prime prime indices is given by A257994.
The number of nonprime prime indices is given by A330944.
Sequence in context: A079374 A353579 A236217 * A260488 A190808 A359727
KEYWORD
nonn
AUTHOR
Gus Wiseman, Oct 18 2018
STATUS
approved